Kevin is 2 times as old as Daniel. Twenty years ago, Kevin was 6 times as old as Daniel. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $k = 2d$ Twenty years ago, Kevin was $k - 20$ years old, and Daniel was $d - 20$ years old. The information in the second sentence can be expressed in the following equation: $k - 20 = 6(d - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = 2d$ . Substituting this into our second equation, we get: $2d$ $-$ $20 = 6(d - 20)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $2 d - 20 = 6 d - 120$ Solving for $d$ , we get: $4 d = 100.$ $d = 25$.